Score-based generative models achieve minimax optimal W1 rates n^{-(β+1)/(2β+d)} over β-Hölder densities, up to polylog factors.
Nonparametric estimation of a factorizable density using diffusion models.arXiv preprint arXiv:2501.01783,
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Generalization bounds for score-based generative models: a synthetic proof
Score-based generative models achieve minimax optimal W1 rates n^{-(β+1)/(2β+d)} over β-Hölder densities, up to polylog factors.